Abstract Gravitational microlensing provides a powerful tool to search for extrasolar planets of stars at distances of order of several kpc. The suspicion of a planetary signal in the two high magnica-tion events OGLE 2006-BLG-245 and MOA 2006-BLG-099 led us to perform a detailed mod-elling and analysis of those two events. Based on the comparison of single-lens and binary-lens models, we demonstrate that the observed light curve deviations are not caused by a planetary companion. Ourmodelling and analysis of four other high magnication events illustrate the possibility to study detection efciencies of microlensing data sets to planetary companions. We also present a detailed study of the single-lens OGLE 2004-BLG-482 microlensing event, used to measure the brightness prole of the background lensed star located in the Galactic bulge. We performed data reduction and analysis of well sampled observations of this event obtained by the PLANET, OGLE and MicroFUN collaborations in theI,Rand clear lters. We also used a high resolution spectrum obtained with VLT/UVES close to the peak of the light curve to determine the fundamental parameters of the source star, that we nd to be a cool red M3 giant withTeff=3667± log150 K,g=21±10. We then performed a detailed microlensing modelling of the light curve to measure linear limb-darkening coefcients and to provide new diagnostics of such measurements through microlensing. We compare our results to model-atmosphere predictions based on limb-darkening coefcients for the corresponding stellar parameters. Our limb-darkening measurements agree very well with predictions of the model atmosphere, for both linear limb-darkening laws and alternative limb-darkening proles based on a principal component analysis of ATLAS stellar atmosphere models.

In 1915, the theory of General Relativity by Einstein brought for the rst time the proof that a massive body could inuence the path of light rays. Some of the most popular manifestation of light deection are the images of distant galaxies which are distorted into giant luminous arcs.“Gravitationallensinghassincebecomeaveryfruiftulbranchofastrophysics,revealing the presence of dark objectsviatheir mass, or magnifying the ux of objects at cosmological distances, such as quasars (e.g. Walsh et al. 1979,for the rst observed lensed quasar, Q 0957+ 561A,B). In 1936, Einstein considered a conguration where two starsin the Milky Way are almost exactly aligned with an observer, and found that the background star would be seen as a bright ring (the “Einstein ring). However, he concluded that the nowadays so-called “microlensing effect would never be detectable, because the angular dimension of the Einstein ring is much too small(around half of a milliarcsec). But fty years later, in 1986, Paczyn´ski published a fundamental article where he proposed a strategy which allow the detection of microlensing eventstowardtheMagellanicClouds.Shortlyafter,Mao&Paczy´nski(1991)demonstrated that observing in the direction of the Galactic bulge would also lead to detectable microlensing events. Although a challenging experiment, two main collaborations formed to check these ideas, EROS and MACHO, and succeeded in 1993 in observing the rst ever microlensing events (Alcock et al. 1993; Aubourg et al. 1993). AnotherimportantconclusionofMao&Paczy´nski(1991)wasthatbyprobingthewhole dark content of the Galactic disc, the microlensing technique was also able to detect very small objects, such as extrasolar planets. Once again, predictions were conrmed, and in 2003, the rst planet detected by microlensing (MOA 2003-BLG-53OGLE 2003-BLG-235, Bond et al. 2004) provided the evidence of the strength of gravitational lensing. In 2005, microlensing was pioneer in unveiling a new class of planets, the now on so-called “Super-Earths, by the discov-ery of OGLE 2005-BLG-390Lb, a rocky and icy∼55M⊕planet. These rocky planets of mass around 2−20M⊕ 2008, microlensing Inare currently major targets of planet search projects. has conrmed its potency to discover very low-mass planets with the detection of MOA-2007-BLG-192Lb (Bennett et al. 2008), a∼33M⊕. All the planets discovered by microlensing are located at several kpc, where no other method is able to probe the planet population. Galactic gravitational microlensing is also one of a few techniques, together with interfer-ometry, transiting extrasolar planets and eclipsing binaries to measure brightness proles. This aspect in stellar astrophysics is very original in the sense it allows to probe the atmosphere of

3

4

stars located in the Galactic bulge, in particular red giants.

1.Introduction

In this thesis, we have studied two aspects of Galactic gravitational microlensing: high magni-cation events to detect the presence of extrasolar planets, and measuring the limb-darkening prole of Bulge stars by using the microlensing effect as a tool.

To understand better the lensing phenomenon, we rst introduce in Chapter 2 the important concepts which will enter in the discussion throughout the thesis. The data reduction process using the difference imaging technique is presented in Chapter 3. The PLANET collaboration of which I am a member and its world-wide network of telescopes are also described. In Chapter 4, we introduce binary and planetary microlensing, and discuss in more detail the case of high magnication events to search for extrasolar planets. The core of the chapter is dedicated to the analysis of six promising high magnication events from theobservational season 2006, includ-ing two interesting candidates which were suspected to hide a planetary signal. In Chapter 5, we perform a detailed analysis of the microlensing event OGLE 2004-BLG-482, to derive precise limb-darkening measurements of the background giant bulge star, that we have compared to stellar atmosphere models. Such microlensing are relatively rare, but contain unique informa-tion of stellar atmospheres and opportunity to test atmosphere models. We nally summarise and conclude in Chapter 6, and underline some of the most promising goals that microlensing can achieve in the future, and how.

Chapter 2

A Review of Gravitational Lensing

We hope this chapter acquaints with a few important questions of gravitational lensing phe-nomenon and presents a briey review of them.

2.1 Gravitational lensing A light ray that passes a massive object, undergoes the deection due to the gravitational po-tential of that mass. The most simple case of lens is a point with massMwhich gravity at a distanceris described by the Newtonian potential 8=−GM GM(2. =− ru2+z21) Assuming the spherically symmetry of a lens object, for the impact parameteruof light ray much larger than the Schwarzschild radius of lens mass, the deection anglea Thus˜ is small. thea˜ can be approximated by integration along unperturbed ray z (see Fig. 2.1) which yields a˜(u) =4cGM2(u)1u(2.2) whereGis the gravitational constant,M(u)is the deecting mass enclosed within radiusuand uthe impact parameter which indicates the minimum approach distance to the object ofis M mass andcis the speed of light. Most of light deection is assumed to occur within the distancezwhich is much smaller than these ones between an observer and lens and between a lens and source. Thus the lens can be considered a thin sheet and in the plane of it the lens mass distribution is projected (the thin-lens approximation). The mass of lens sheet is characterised by its surface mass densityS S(~u) =ZΛ(~uz)dz(2.3)

2.2 The lens equation To imagine how the gravitational lensing phenomenon happens, the geometric description of it with a single lens illustrated in Fig. 2.2 can be helpful. From this sketch using the Euclidean